math.h

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/* -*- c++ -*- */
/*
 * Copyright 2003,2005,2008,2013 Free Software Foundation, Inc.
 *
 * This file is part of GNU Radio
 *
 * GNU Radio is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3, or (at your option)
 * any later version.
 *
 * GNU Radio is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with GNU Radio; see the file COPYING.  If not, write to
 * the Free Software Foundation, Inc., 51 Franklin Street,
 * Boston, MA 02110-1301, USA.
 */

/*
 * mathematical odds and ends.
 */

#ifndef _GR_MATH_H_
#define _GR_MATH_H_

#include <cmath>
#include <gnuradio/api.h>
#include <gnuradio/gr_complex.h>

namespace gr {

  static inline bool
  is_power_of_2(long x)
  {
    return x != 0 && (x & (x-1)) == 0;
  }

  /*!
   * \brief Fast arc tangent using table lookup and linear interpolation
   * \ingroup misc
   *
   * \param y component of input vector
   * \param x component of input vector
   * \returns float angle angle of vector (x, y) in radians
   *
   * This function calculates the angle of the vector (x,y) based on a
   * table lookup and linear interpolation. The table uses a 256 point
   * table covering -45 to +45 degrees and uses symetry to determine
   * the final angle value in the range of -180 to 180 degrees. Note
   * that this function uses the small angle approximation for values
   * close to zero. This routine calculates the arc tangent with an
   * average error of +/- 0.045 degrees.
   */
  GR_RUNTIME_API float fast_atan2f(float y, float x);

  static inline float
  fast_atan2f(gr_complex z)
  {
    return fast_atan2f(z.imag(), z.real());
  }

  /* This bounds x by +/- clip without a branch */
  static inline float
  branchless_clip(float x, float clip)
  {
    float x1 = fabsf(x+clip);
    float x2 = fabsf(x-clip);
    x1 -= x2;
    return 0.5*x1;
  }

  static inline float
  clip(float x, float clip)
  {
    float y = x;
    if(x > clip)
      y = clip;
    else if(x < -clip)
      y = -clip;
    return y;
  }

  // Slicer Functions
  static inline unsigned int
  binary_slicer(float x)
  {
    if(x >= 0)
      return 1;
    else
      return 0;
  }

  static inline unsigned int
  quad_45deg_slicer(float r, float i)
  {
    unsigned int ret = 0;
    if((r >= 0) && (i >= 0))
      ret = 0;
    else if((r < 0) && (i >= 0))
      ret = 1;
    else if((r < 0) && (i < 0))
      ret = 2;
    else
    ret = 3;
    return ret;
  }

  static inline unsigned int
  quad_0deg_slicer(float r, float i)
  {
    unsigned int ret = 0;
    if(fabsf(r) > fabsf(i)) {
      if(r > 0)
        ret = 0;
      else
        ret = 2;
    }
    else {
      if(i > 0)
        ret = 1;
      else
        ret = 3;
    }

    return ret;
  }

  static inline unsigned int
  quad_45deg_slicer(gr_complex x)
  {
    return quad_45deg_slicer(x.real(), x.imag());
  }

  static inline unsigned int
  quad_0deg_slicer(gr_complex x)
  {
    return quad_0deg_slicer(x.real(), x.imag());
  }

  // Branchless Slicer Functions
  static inline unsigned int
  branchless_binary_slicer(float x)
  {
    return (x >= 0);
  }

  static inline unsigned int
  branchless_quad_0deg_slicer(float r, float i)
  {
    unsigned int ret = 0;
    ret =  (fabsf(r) > fabsf(i)) * (((r < 0) << 0x1));       // either 0 (00) or 2 (10)
    ret |= (fabsf(i) > fabsf(r)) * (((i < 0) << 0x1) | 0x1); // either 1 (01) or 3 (11)

    return ret;
  }

  static inline unsigned int
  branchless_quad_0deg_slicer(gr_complex x)
  {
    return branchless_quad_0deg_slicer(x.real(), x.imag());
  }

  static inline unsigned int
  branchless_quad_45deg_slicer(float r, float i)
  {
    char ret = (r <= 0);
    ret |= ((i <= 0) << 1);
    return (ret ^ ((ret & 0x2) >> 0x1));
  }

  static inline unsigned int
  branchless_quad_45deg_slicer(gr_complex x)
  {
    return branchless_quad_45deg_slicer(x.real(), x.imag());
  }

  /*!
   * \param x any value
   * \param pow2 must be a power of 2
   * \returns \p x rounded down to a multiple of \p pow2.
   */
  static inline size_t
  p2_round_down(size_t x, size_t pow2)
  {
    return x & -pow2;
  }

  /*!
   * \param x any value
   * \param pow2 must be a power of 2
   * \returns \p x rounded up to a multiple of \p pow2.
   */
  static inline size_t
  p2_round_up(size_t x, size_t pow2)
  {
    return p2_round_down(x + pow2 - 1, pow2);
  }

  /*!
   * \param x any value
   * \param pow2 must be a power of 2
   * \returns \p x modulo \p pow2.
   */
  static inline size_t
  p2_modulo(size_t x, size_t pow2)
  {
    return x & (pow2 - 1);
  }

  /*!
   * \param x any value
   * \param pow2 must be a power of 2
   * \returns \p pow2 - (\p x modulo \p pow2).
   */
  static inline size_t
  p2_modulo_neg(size_t x, size_t pow2)
  {
    return pow2 - p2_modulo(x, pow2);
  }

} /* namespace gr */

#endif /* _GR_MATH_H_ */